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CBSE Class 12 Maths 2010 Solved Paper

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Question : 3 of 29
Marks: +1, -0
What is the principal value of cos⁡−1(−32)\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) ?
Solution:  
Let cos⁡−1(−32)\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) = x
⇒ cos x = - 32\frac{\sqrt{3}}{2}
⇒ cos x = - cos (π6)\left(\frac{\pi}{6}\right)
⇒ cos x = cos (π−π6)\left(\pi - \frac{\pi}{6}\right)
⇒ cos x = cos (5π6)\left(\frac{5\pi}{6}\right)
⇒ x = 5π6\frac{5\pi}{6}
Therefore, the principal value of cos⁡−1(−32)\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) is 5π6\frac{5\pi}{6}
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